Ieee81 1983

i
ANSI/IEEE Std 81-1983
(Revision of IEEE Std 81-1962)
An American National Standard
IEEE Guide for Measuring Earth
Resistivity, Ground Impedance, and
Earth Surface Potentials of a Ground
System
Sponsor
Power System Instrumentation and Measurements Committee
of the
IEEE Power Engineering Society
Approved September17, 1981
IEEE Standards Board
Approved September 4, 1984
American National Standards Institute
© Copyright 1983 by
The Institute of Electrical and Electronics Engineers, Inc
345 East 47th Street, New York, NY 10017, USA
No part of this publication may be reproduced in any form, in an electronic retrival system or otherwise, without the
prior written permission of the publisher.
Authorized licensed use limited to: INACAP. Downloaded on November 10,2021 at 15:01:27 UTC from IEEE Xplore. Restrictions apply.

ii
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iii
Foreword
(This Foreword is not a part of IEEE Std 81-1983, IEEE Guide for Measuring Earth Resistivity, Ground Impedance, and Earth
Surface Potentials of a Ground System.)
In order to increase its practical usefulness, this guide has been divided into two parts. Part I, Normal Measurements,
covers the majority of field measurements which do not require special high-precision equipment and measuring
techniques, and which do not encounter unusual difficulties such as may be found with extensive grounding systems,
abnormally high stray ac or de currents, etc. Part I has been extensively revised and updated. Part II, Special
Measurements, is to be completed in the future. This part is intended to describe the methods of measurements
applicable when unusual difficulties make normal measurements either impractical or inaccurate. Very large power
station ground grids and counterpoises of transmission lines are examples of such grounding systems.
This guide was prepared by the Earth Resistivity, Ground Impedance, and Earth Surface Potential ,Measurement
Working Group of the RLC Subcommittee, Power System Instrumentation and Measurements Committee. The
working group's members at the time the guide was prepared were:
D. Mukhedkar, Chair
F. Dawalibi, Secretary
G. Y. R. Allen
M. J. Anna
E. B. Curdts†
R. D. Crosier
W. K. Dick
W. G. Finney
J. L. Hayes†
R. Hall
R. J. Heh
J. F. Laidig
A. C. Legates
R. Malewski
H. C. Ramberg
B. Stanleigh
F. P. Zupa
†Deceased
W. J. Lyon (Liaison member
with 80-1976.)
W. K. Switzer (Liaison with
Substations Committee.)
When the IEEE Standards Board approved this standard on September 17, 1981, it had the following membership:
I. N. Howell, Jr, Chair
Irving Kolodny, Vice Chair
Sara I. Sherr, Secretary
G. Y. R. Allen
J. J. Archambault
J. H. Beall
J. T. Boettger
Edward Chelotti
Edward J. Cohen
Len S. Corey
Jay Forster
Kurt Greene
Loering M. Johnson
Joseph L. Koepfinger
J. E. May
Donald T. Michael*
J. P. Riganati
F. Rosa
R. W. Seelbach
J. S. Stewart
W. E. Vannah
Virginius N. Vaughan, Jr
Art Wall
Robert E. Weiler
* Member emeritus

iv
CLAUSE PAGE
1. Purpose................................................................................................................................................................1
1.1 .................................................................................................................................................................... 1
1.2 .................................................................................................................................................................... 1
2. Scope...................................................................................................................................................................2
2.1 .................................................................................................................................................................... 2
2.2 .................................................................................................................................................................... 2
2.3 .................................................................................................................................................................... 2
3. Objectives of Tests..............................................................................................................................................2
3.1 .................................................................................................................................................................... 2
3.2 .................................................................................................................................................................... 2
3.3 .................................................................................................................................................................... 2
4. Definitions...........................................................................................................................................................3
5. Safety Precautions While Making Ground Tests................................................................................................4
5.1 Station Ground Tests.................................................................................................................................. 4
5.2 Surge-Attester Ground Tests...................................................................................................................... 5
5.3 Small Isolated Ground Tests...................................................................................................................... 5
6. General Considerations of the Problems Related to Measurements...................................................................5
6.1 Complexities .............................................................................................................................................. 5
6.2 Test Electrodes........................................................................................................................................... 5
6.3 Stray Direct Currents ................................................................................................................................. 6
6.4 Stray Alternating Currents ......................................................................................................................... 7
6.5 Reactive Component of Impedance of a Large Grounding System........................................................... 7
6.6 Coupling Between Test Leads ................................................................................................................... 7
6.7 Buried Metallic Objects ............................................................................................................................. 7
7. Earth Resistivity..................................................................................................................................................8
7.1 General....................................................................................................................................................... 8
7.2 Methods of Measuring Earth Resistivity ................................................................................................. 10
7.3 Interpretation of Measurements ............................................................................................................... 13
7.4 Instrumentation ........................................................................................................................................ 16
8. Ground Impedance............................................................................................................................................16
8.1 General..................................................................................................................................................... 16
8.2 Methods of Measuring Ground Impedance.............................................................................................. 18
8.3 Testing the Integrity of the Ground Grid ................................................................................................. 23
9. Earth Potential...................................................................................................................................................24
9.1 Equipotential Lines .................................................................................................................................. 24
9.2 Potential Contour Surveys ....................................................................................................................... 25
9.3 Step and Touch Voltages ......................................................................................................................... 25

v
CLAUSE PAGE
10. Transient Impedance.........................................................................................................................................27
10.1 Transient Impedance of Ground Systems ................................................................................................ 27
11. Model Tests.......................................................................................................................................................29
11.1 Purpose..................................................................................................................................................... 29
11.2 Similarity Criteria and Limitations .......................................................................................................... 29
11.4 Resistance Measurements ........................................................................................................................ 30
11.5 Potential Measurements ........................................................................................................................... 30
11.6 Interpretation of Measurements ............................................................................................................... 30
12. Instrumentation .................................................................................................................................................31
12.1 Ratio Ohmmeter....................................................................................................................................... 31
12.2 Double-Balance Bridge............................................................................................................................ 32
12.3 Single-Balance Transformer .................................................................................................................... 33
12.4 Ammeter-Voltmeter................................................................................................................................. 34
12.5 Induced Polarization Units....................................................................................................................... 34
12.6 High-Frequency Earth Resistance Meter ................................................................................................. 35
13. Practical Aspects of Measurements ..................................................................................................................36
13.1 Selection of Auxiliary Electrodes ............................................................................................................ 36
13.2 Selection of Test Leads............................................................................................................................ 37
13.3 Selection of Auxiliary Equipment............................................................................................................ 37
13.4 Testing Precautions.................................................................................................................................. 38
13.5 Large Substations..................................................................................................................................... 39
Annex A Nonuniform Soils (Informative)....................................................................................................................40
Annex B Determination of an Earth Model (Informative)............................................................................................42
Annex C Theory of the Fall of Potential Method (Informative)...................................................................................44
Annex D Bibliography (Informative)............................................................................................................................47

Copyright © 1983 IEEE All Rights Reserved 1
IEEE Guide for Measuring Earth
Resistivity, Ground Impedance, and
Earth Surfact Potentials of a Ground
System and
Part I Normal Measurements
1. Purpose
1.1
It is the purpose of this guide to describe and discuss the present state of the technique of measuring ground resistance
and impedance, earth resistivity, potential gradients from currents in the earth, and the prediction of the magnitudes of
ground resistance and potential gradients from scale model tests. Factors influencing the choice of instruments and the
techniques for various types of measurements are covered. These include the purpose of the measurement, the
accuracy required, the type of instruments available, possible sources of error, and the nature of the ground or
grounding system under test.
1.2
The guide is intended to assist the engineer or technician in obtaining and interpreting accurate, reliable data. It
describes test procedures which promote the safety of personnel and property, and prevent interference with the
operation of neighboring facilities.

2 Copyright © 1983 IEEE All Rights Reserved
IEEE Std 81-1983 IEEE GUIDE FOR MEASURING EARTH RESISTIVITY, GROUND IMPEDANCE,
2. Scope
2.1
The testing methods covered in this guide include:
1) The measurement of the resistance and impedance to earth of electrodes varying from small rods and plates
to large grounding systems of stations.
2) Ground. potential surveys, including the measurement of step and touch voltages, and potential contour
surveys.
3) Scale-model tests for laboratory determination of the ground resistance and potential gradients for an
idealized design.
4) The measurement of earth resistivity.
2.2
The methods covered herein are limited to those using direct current, periodically reversed direct current, alternating
sinusoidal current and impulse currents (for measuring transient impedances). This guide does not propose to cover all
possible test signals and test methods.
2.3
Extreme precision is not always possible because of the many variables encountered; therefore, the measurements
should be carefully made by the most suitable method available, with a thorough understanding of the possible sources
of error.
3. Objectives of Tests
3.1
Measurements of ground resistance or impedance and potential gradients on the surface of the earth due to ground
currents are necessary to:
1) Verify the adequacy of a new grounding system
2) Detect changes in an existing grounding system
3) Determine hazardous step and touch voltages
4) Determine ground potential rise (GPR) in order to design protection for power and communication circuits.
3.2
Scale-model tests are useful in studying or developing new designs for grounding systems which cannot be adequately
studied by analytical methods (complex shape or complex soil structure).
3.3
Earth resistivity measurements are useful for:
1) Estimating the ground resistance of a proposed substation or transmission tower
2) Estimating potential gradients including step and touch voltages
3) Computing the inductive coupling between neighboring power and communication circuits

AND EARTH SURFACE POTENTIALS OF A GROUND SYSTEM IEEE Std 81-1983
4) Designing cathodic protection systems
5) Geological surveys
4. Definitions
Definitions of terms pertinent to the subject matter are listed here. Those approved or standardized by other bodies are
used wherever possible.
Definitions as given herein apply specifically to the application of this guide. For additional definitions see ANSI/IEEE
Std 100-1977, IEEE Standard Dictionary of Electrical and Electronics Terms.
ground: A conducting connection, whether intentional or accidental, by which an electric circuit or equipment is
connected to the earth, or to some conducting body of relatively large extent that serves in place of the earth.
NOTE — It is used for establishing and maintaining the potential of the earth (or of the conducting body) or approximately that
potential, on conductors connected to it, and for conducting ground current to and from the earth (or the conducting
body).
grounded: A system, circuit, or apparatus referred to is provided with a ground.
ground-return circuit: A circuit in which the earth is utilized to complete the circuit.
ground current: Current flowing in the earth or in a grounding connection.
grounding conductor: The conductor that is used to establish a ground and that connects an equipment, device,
wiring system, or another conductor (usually the neutral conductor) with the grounding electrode or electrodes.
grounding electrode: A conductor used to establish a ground.
grounding connection: A connection used in establishing a ground and consists of a grounding conductor, a
grounding electrode and the earth (soil) that surrounds the electrode or some conductive body which serves instead of
the earth.
ground grid: A system of grounding electrodes consisting of interconnected bare cables buried in the earth to provide
a common ground for electrical devices and metallic structures.
NOTE — It may be connected to auxiliary grounding electrodes to lower its resistance.
ground mat: A system of bare conductors, on or below the surface of the earth, connected to a ground or a ground grid
to provide protection from dangerous touch voltages.
NOTE — Plates and gratings of suitable area are common forms of ground mats.
grounding system: Consists of all interconnected grounding connections in a specific area.
ground resistance (grounding electrode): The ohmic resistance between the grounding electrode and a remote
grounding electrode of zero resistance.
NOTE — By remote is meant at a distance such that the mutual resistance of the two electrodes is essentially zero.
mutual resistance of grounding electrodes: Equal to the voltage change in one of them produced by a change of one
ampere of direct current in the other, and is expressed in ohms.
electric potential: The potential difference between the point and some equipotential surface, usually the surface of
the earth, which is arbitrarily chosen as having zero potential (remote earth).
NOTE — A point which has a higher potential than a zero surface is said to have a positive potential; one having a lower potential
has a negative potential.
equipotential line or contour: The locus of points having the same potential at a given time.
potential profile: A plot of potential as a function of distance along a specified path.

surface-potential gradient: The slope of a potential profile, the path of which intersects equipotential lines at right
angles.
touch voltage: The potential difference between a grounded metallic structure and a point on the earth's surface
separated by a distance equal to the normal maximum horizontal reach, approximately one meter.
step voltage: The potential difference between two points on the earth's surface, separated by a distance of one pace,
that will be assumed to be one meter, in the direction of maximum potential gradient.
NOTE — This potential difference could be dangerous when current flows through the earth or material upon which a workman is
standing, particularly under fault conditions.
resistivity (material): A factor such that the conduction-current density is equal to the electric field in the material
divided by the resistivity.
coupling: The association of two or more circuits or systems in such a way that power or signal information may be
transferred from one to another.
NOTE — Coupling is described as close or loose. A close-coupled process has elements with small phase shift between specified
variables; close-coupled systems have large mutual effect shown mathematically by cross-products in the system matrix.
coupling capacitance: The association of two or more circuits with one another by means of capacitance mutual to the
circuits.
resistive coupling: The association of two or more circuits with one another by means of resistance mutual to the
circuits.
direct coupling: The association of two or more circuits by means of self-inductance, capacitance, resistance, or a
combination of these that is common to the circuits.
inductive coupling (1) (communication circuits): The association of two or more circuits with one another by means
of inductance mutual to the circuits or the mutual inductance that associates the circuits.
NOTE — This term, when used without modifying words, is commonly used for coupling by means of mutual inductance,
whereas coupling by means of self-inductance common to the circuits is called direct inductive coupling.
(2) (inductive coordination practice): The interrelation of neighboring electric supply and communication circuits
by electric or magnetic induction, or both.
effective resistivity: A factor such that the conduction current density is equal to the electric field in the material
divided by the resistivity.
counterpoise (overhead lines) (lighting protection): A conductor or system of conductors, arranged beneath the
transmission line, located on, above or most frequently below the surface of the earth, and connected to the footings of
the towers or poles supporting the line.
5. Safety Precautions While Making Ground Tests
5.1 Station Ground Tests
It should be strongly impressed on all test personnel that a lethal potential can exist between the station ground and a
remote ground if a power-system fault involving the station ground occurs while ground tests are being made.
Since one of the objectives of tests on a station-ground system is to establish the location of remote earth for both
current and potential electrodes, the leads to these electrodes must be treated as though a possible potential could exist
between test leads and any point on the station ground grid. Some idea of the magnitude of this possible potential may
be gained from the consideration that even in the larger stations the ground grid shall have an impedance in the order
of 0.05 Ω to 0.5Ω. Assuming for this example that the ground-fault current through the grid is in the order of 20 kA the
potential to remote earth (ground potential rise) will be in the order of 1.0 kV to 10 kV. For higher ground impedance
or greater fault currents, the rise of station-ground voltage may exceed 10 kV.

The preceding discussion points to the necessity of caution when handling the test leads, and under no circumstances
should the two hands or other parts of the body be allowed to complete the circuit between points of possible high-
potential difference. It is true that the chances are remote that a station-ground fault will occur while test leads are
being handled, but this possibility should not be discounted and therefore the use of insulating shoes, gloves, blankets,
and other protection devices are recommended whenever measurements are carried out at an energized power station.
In all cases, safety procedures and practices adopted by the particular organization involved shall be followed.
5.2 Surge-Attester Ground Tests
These grounds fall in a special category because of the extremely high short-duration lightning currents carried by
surge-arrester grounds. These currents may be in excess of 50 000 A for surge currents, with a possibility of fault-
system currents in the case of a defective surge arrester. An isolated surge arrester ground should never be
disconnected to be measured, since the base of the arrester can be elevated to the line potential.A surge-arrester ground
can be tested as long as precautions axe taken to minimize arrester discharge.
5.3 Small Isolated Ground Tests
Another precaution concerns possible high-potential gradients around the current electrode. If current is passed into a
remotely located electrode, as in the fall-of-potential method, it is worthwhile to ensure against a curious person being
allowed near the current electrode while tests are in progress. Similarly, in rural areas grazing animals should not be
allowed near the test current electrode.
6. General Considerations of the Problems Related to Measurements
6.1 Complexities
The measurements of earth resistivities, ground impedances, and potential gradients introduce a number of
complexities not encountered in other resistance, impedance, and potential measurements.
It may be necessary to make multiple measurements and to plot trends. Stray currents and other factors usually
interfere with the measurements.
With development and industrial growth adjacent to power substations, it becomes increasingly difficult to choose a
suitable direction or locations for test probes to make a resistance test. Moreover, the connection of overhead ground
wires, buried water pipes, cable sheaths, etc, all have the effect of physically distorting and enlarging the ground grid.
NOTE — Overhead ground wires may be insulated either deliberately or by clamp corrosion and therefore low-voltage tests may
give answers different from actual fault tests.
Ground impedance measurements should be made immediately after the ground grid has been installed to be certain
that there are no major omissions of grounded components normally connected into the ground grid. Future
installations such as water pipes, rail, etc will alter the values.
It should be noted, however, that the ground impedance will usually decrease as the earth settles to a uniform
compactness perhaps a year after installation.
6.2 Test Electrodes
The ground-impedance measurement methods described in the following sections require the use of current and
voltage test electrodes.

If the impedance measurement method used is the two- or three-point method, the impedance of the test electrodes
should be either negligible with respect to that of the ground being tested (two-point method) or of the same order of
magnitude as the ground being tested (three-point method). Otherwise, incorrect results may be obtained.
Obviously, these restrictions limit the use of such methods to grounds of relatively small extent such as residential
swimming pools and small low-voltage distribution substation grounds.
In the case of impedance measurements using the fall-of-potential method, the requirements of the test electrodes are
not so critical.
Theoretically the ground resistances of the test electrodes do not influence the measurements since these are taken into
consideration by the method of measurement. In practice, however, the resistance values should not exceed a
maximum value beyond which there is insufficient test current in the measuring instrument. By insufficient test current
is meant:
1) Current lower than the instrument sensitivity, or
2) Current in the order of magnitude of the stray currents in the earth
3) Or both (1) and (2)
In case (1), the only corrective action available at the site of measurement is to increase the test current. This can be
done by either increasing the voltage of the power supply or by decreasing the test electrode resistances. Increasing the
power supply voltage is not always possible especially with hand-driven generators incorporated in the measuring
instrument. When this solution is practical, care must be taken to avoid dangerous potentials of the electrodes and test
leads. A maximum of 100 V is considered safe if special precautions (such as use of insulating gloves or shoes) are
taken.
Often the most effective way of increasing the test current is to decrease the current electrode resistance. This can be
done by driving the rod deeper into the soil, pouring water around the rod, or by driving additional rods and
interconnecting them in parallel. The addition of salt to the water poured around the test electrodes is of very little
value; the moisture is the main requirement.
As a general rule the resistance values of the current and potential electrodes should meet the requirements of the
instruments used. With commercial instruments, a potential electrode resistance of 1000 Ω may be used. Some
manufacturers claim that their instrument will permit 10 000 Ω in the potential electrode.
The current electrode resistance should usually be less than 500 Ω. This resistance value is a function of the voltage
generated by the power supply and the desired test current. The ratio of the generated voltage to the current electrode
resistance determines the test current flowing in the current-indicating element of the instrument being used. As a rule
of thumb the ratio between the current electrode resistance and the ground resistance being tested should never exceed
1000 to 1, preferably 100 to 1 or less.
In case (2), when dc tests are being made, the test current must be increased to overcome the interfering effects of stray
dc earth currents. When tests with ac or periodically reversed dc signals axe being made, the frequency of the test
signal may be set to a frequency not present in the stray currents.
6.3 Stray Direct Currents
Conduction of electricity in the soil is electrolytic and direct current results in chemical action and polarization
potential difference. Direct potentials are produced between various types of soil and between soil and metal by
galvanic action. Galvanic potentials, polarization, and, if present, stray direct currents may seriously interfere with
direct-current measurements. Therefore, periodically reversed direct current or sometimes a regularly pulsed current is
used in making measurements. However, when using periodically reversed direct current for resistance measurements

the resulting values will be fairly close, but they may not be accurate for alternating-current applications. Caution must
be exercised in areas subject to solar-induced currents (quasi-dc).
6.4 Stray Alternating Currents
Stray alternating currents in the earth, in the grounding system under test, and in the test electrodes present an
additional complication. The effects of stray alternating current may be mitigated in ground resistance measurements
by utilizing a frequency that is not present in the stray current. Most measuring devices use frequencies within a range
of 50 Hz to 100 Hz. The use of filters or narrow band measuring instruments, or both, is often required to overcome the
effects of stray alternating currents.
6.5 Reactive Component of Impedance of a Large Grounding System
The impedance of a large grounding system may be extremely low (for example, 0.010 Ω) but it may have a significant
quadrature component [B23]1. Certain precautions should be taken when measuring the 60 Hz impedance of a large
grounding system. For such measurements the test device should be operated at an approximate system frequency of
60 Hz, but the test frequency should be slightly above or below 60 Hz, using a minimum of 50 A for the most accurate
results and to avoid 60 Hz ground currents. Part II of this guide2
, Special Measurements, will cover impedance
measurements of large grounding systems.
6.6 Coupling Between Test Leads
The effect of coupling between the test leads becomes important when measuring low values of ground impedance.
Any voltage produced in the potential lead due to coupling from current flowing in the current lead is directly additive
to the desired measured voltage and produces a measurement error. Since the 60 Hz inductive coupling between two
parallel test leads may be as high as 0.1 Ω/100 m, the error can be appreciable. Low ground impedance usually is found
with a large area ground, which requires long test leads to reach remote earth.
Conversely, a small area ground usually has fairly high ground impedance and requires shorter test leads to reach
remote earth. Thus the effects of coupling can be expected to be worse on measurements of large area, low impedance
grounds. As a rule of thumb test lead coupling is usually negligible on measurements of grounds of 10 Ω or greater, is
almost always important on measurements of 1 Ω or less, and should be considered in the range between 1 and 10 Ω.
Test lead coupling may be minimized by appropriately routing the potential and current leads. When test lead
couplings are anticipated, the potential and current leads should be placed at the maximum feasible angle.
6.7 Buried Metallic Objects
Partially or completely buried objects such as rails, water, or other industrial metallic pipes will considerably influence
the measurement results [B9], [B36].
In earth-resistivity tests a sharp drop in the measured value is often caused by the presence of a metallic object buried
close to the test location. The magnitude and extent of the drop gives an idea of the importance and depth of the buried
material. The measured resistance of a ground electrode located close to a buried metallic object can be significantly
lower than its value if the additional buried metal objects were not present. However, the importance of the effect of
buried metallic structures should not be minimized in determining the effective GPR for communication protective
purpose. Earth potential contours are distorted and gradients are increased when measured above buried metallic
objects.
1The numbers in brackets correspond to those of the Bibliography listed in Appendix D of this guide.
2Part II of this guide has not been completed at this time.

Wherever the presence of buried metallic structures is suspected in the area where soil resistivity measurements are to
be taken and the location of these structures is known, the influence of these structures on the soil resistivity
measurement results can be minimized by aligning the test probes in a direction perpendicular to the routing of these
structures. Also the location of the test probes should be as far as possible from the buried structures.
7. Earth Resistivity
7.1 General
The techniques for measuring soil resistivity are essentially the same whatever the purpose of the measurement.
However, the interpretation of the recorded data can vary considerably, especially where soils with non-uniform
resistivities are encountered. The added complexity caused by nonuniform soils is common, and in only a few cases
are the soil resistivities constant with increasing depth.
Earth resistivity varies not only with the type of soil but also with temperature, moisture, salt content, and compactness
(see Fig 1). The literature indicates that the values of earth resistivity vary from 0.01 to 1 Ω.m for sea water and up to
109 Ω.m for sandstone. The resistivity of the earth increases slowly with decreasing temperatures from 25 °C to 0 °C.
Below 0 °C the resistivity increases rapidly. In frozen soil, as in the surface layer in winter the resistivity may be
exceptionally high.
Table 1 shows the resistivity values for various soils and rocks. This table has the advantage of being simple. More
detailed tables are available in [B31], [B36], [B39].
Usually there are several layers, each having a different resistivity. Lateral changes may also occur, but in general,
these changes are gradual and negligible at least in the vicinity of the site concerned.
In most cases, the measurement will show that the resistivity ρa, is mainly a function of depth z. For purposes of
illustration, we will assume that this function may be written as:
(1)
The nature of the function Φ is in general not simple and consequently the interpretation of the measurements will
consist of establishing a simple equivalent function Φe which will give the best approximation. In the case of power
and communication circuits, a two horizontal layer configuration [B10], [B18], [B20], [B31], [B38], [B39], and an
exponential earth [B38], [B42] have proved to be good approximations that can be useful in determining system
designs.
Some publications [B9], [B10], [B18], [B20], [B31], [B36], [B38], [B39], [B42], have shown that earth surface
potential gradients inside or adjacent to an electrode are mainly a function of top soil resistivity. In contrast, the ground
electrode resistance is primarily a function of deep soil resistivity, especially if the electrode is very large.
NOTE — This is not valid in those extreme cases where the electrode is buried in an extremely high resistivity top soil.
Transmission-line parameters at power frequencies are sensitive to the presence of layers of different resistivities.
However, at power-line carrier frequencies, radio, or surge frequencies, earth return impedances are practically
sensitive only to the top few meters of soil.
The above statements are good arguments in favor of methods which include both surface and deep soft-resistivity
measurements. In such methods a number of readings are taken. At each reading the test current involves an increased
volume of the surrounding earth.
ρa φ z
( )
=

Figure 1—Earth Resistivity Variations
(a) Salt (b) Moisture (c) Temperature

Table 1—Geological Period and Formation
7.2 Methods of Measuring Earth Resistivity
7.2.1 Geological Information and Soil Samples
Often, at the site where a grounding system is to be installed, extensive civil engineering work must be carried out.
This work usually involves geological prospecting which results in a considerable amount of information on the nature
and configuration of the site soft. Such data could be of considerable help to the electrical engineer who should try to
obtain this information.
The determination of soft resistivity from the values of resistance measured between opposite faces of a soil sample of
known dimensions is not recommended since the unknown interfacial resistances of the soil sample and the electrodes
are included in the measured value.
Earth Resistivity
Ohmmeters Quarternary
Cretaceous
Tertiary
Quarternary
Carboniferous
Triassic
Cambrian
Ordovician
Devonian
Pre-Cambrian
andCombinat.
with Cambrian
1 Sea water
Loam
10 Unusually low Clay
Chalk Chalk
30 Very low
Trap
100 Low Diabase
Shale
300 Medium Shale
Limestone
Limestone
1000 High Sandstone
Sandstone Sandstone
Coarse Sand
3000 Very High Dolomite Quartyite
and Gravel
Slate
10 000 Unusally high in surface
Granite
Layers
Gneisses
NOTE — Table 1 is from reference [B38] of the Bibliography section.

A more accurate determination is possible if a four-terminal resistance measurement of the soil sample is made. The
potential terminals should be small, relative to the sample cross-section, and located sufficiently distant from the
current terminals to assure near-uniform current distribution across the sample. A distance equal to the larger cross-
section dimension is usually adequate for the purpose of the determination.
It is difficult, and in some cases impossible, to obtain a useful approximation of soil resistivity from resistivity
measurements on samples. This is due to the difficulty of obtaining representative, homogeneous soil samples, and in
duplicating the original soil compaction and moisture content in the test cell.
7.2.2 Variation of Depth Method
This method, sometimes called a three-point method, is a ground-resistance test carried out several times, each time
the depth of burial of the tested electrode is increased by a given increment. The purpose of this is to force more test
current through the deep soil. The measured resistance value will then reflect the variation of resistivity at increased
depth. Usually the tested electrode is a rod. Rods are preferred to other types of electrodes because they offer two
important advantages:
1) The theoretical value of ground-rod resistance is simple to calculate with adequate accuracy, therefore, the
results are easy to interpret.
2) The driving of a rod into the soft is normally an easy operation.
The above measurements can be carried out using one of the methods described in 8.2. One should bear in mind,
however, that the measured value of the resistance should be as accurate as possible so that it can be successfully
compared to the theoretical value. Therefore, the fall-of-potential method is preferably used for these measurements.
The variation of depth method gives useful information about the nature of soil in the vicinity of the rod (5 to 10 times
the rod length). If a large volume of soil must be investigated, it is preferable to use the four-point method, since the
driving of long rods is not practical.
7.2.3 Two-Point Method
Rough measurements of the resistivity of undisturbed earth can be made in the field with the shepard-soil resistivity
meter and similar two-point methods. The apparatus consists of one small and one smaller iron electrode, both
attached to an insulating rod. The positive terminal of a battery is connected through a milliammeter to the smaller
electrode and the negative terminal to the other electrode. The instrument can be calibrated to read directly in ohm-
centimeters at nominal battery voltage. This type of apparatus is easily portable and with it a number of measurements
can be made in a short time on small volumes of soil by driving the electrodes in the ground or in the walls or bottom
of excavations.
7.2.4 Four-Point Method
The most accurate method in practice of measuring the average resistivity of large volumes of undisturbed earth is the
four-point method [B43]. Small electrodes are buried in four small holes in the earth, all at depth b and spaced (in a
straight line) at intervals a. A test current I is passed between the two outer electrodes and the potential V between the
two inner electrodes is measured with a potentiometer or high-impedance voltmeter. Then V/I gives the resistance R in
ohms.

Two different variations of the four-point method are often used:
1) Equally Spaced or Wenner Arrangement. With this arrangement the electrodes are equally spaced as shown in
Fig 3(a). Let a be the distance between two adjacent electrodes. Then, the resistivity ρ in the terms of the
length units in which a and b are measured is:
(2)
It should be noted that this does not apply to ground rods driven to depth b; it applies only to small electrodes
buried at depth b, with insulated connecting wires. However, in practice, four rods are usually placed in a
straight line at intervals a, driven to a depth not exceeding 0.1 a. Then we assume b = 0 and the formula
becomes:
(3)
and gives approximately the average resistivity of the soil to the depth a.
A set of readings taken with various probe spacings gives a set of resistivities which, when plotted against
spacing, indicates whether there are distinct layers of different soil or rock and gives an idea of their
respective resistivities and depth. (See Fig 2.)
Figure 2—Typical Resistivity Curve
2) Unequally-spaced or Schlumberger-Palmer Arrangement. One shortcoming of the Wenner method is the
rapid decrease in magnitude of potential between the two inner electrodes when their spacing is increased to
relatively large values. Often the commercial instruments are inadequate for measuring such low potential
values. In order to be able to measure resistivities with large spacings between the current electrodes the
arrangement shown in Fig 3(b) can be used successfully. The potential probes are brought nearer the
corresponding current electrodes. This increases the potential value measured.
The formula to be used in this case can be easily determined [B35]. If the depth of burial of the electrodes b
is small compared to their separation d and c, then the measured resistivity can be calculated as follows:
(4)
ρ
4πaR
1
2a
a
2
4b
2
+
------------------------
-
a
a
2
b
2
+
--------------------
-
–
+
-------------------------------------------------------------
-
=
ρ 2πaR
=
ρ πc c d
+
( )R d
⁄
=

Figure 3—Four-Point Method
(a) Equally Spaced (b) Unequally Spaced
7.3 Interpretation of Measurements
The interpretation of the results obtained in the field is perhaps the most difficult part of the measurement program. As
mentioned in 7.1 the earth resistivity variation is great and complex because of the heterogeneity of earth. Except for
very few cases it is essential to establish a simple equivalent to the earth structure. This equivalent depends on:
1) The accuracy and extent of the measurements
2) The method used
3) The complexity of the mathematics involved
4) The purpose of the measurements
For applications in power engineering, the two-layer equivalent model is accurate enough without being
mathematically too involved.
7.3.1 Geological Information and Soil Samples
Special tools or mathematical equations are not necessary to interpret such information which are mainly given in the
figures and tables provided by geological explorations.
7.3.2 Variation of Depth Method (see Appendix B)
The following interpretation assumes that the tested ground is a rod driven at depth l. The rod radius r is small
compared to l. For other forms of electrodes the calculations will be similar to the following:
The ground resistance of the rod buried in a uniform soil is given by reference [B39]:
(5)
or
(6)
R
ρ
2πl
-------
-In
2l
r
----
-
=
R
ρ
2πl
-------
-In
4l
r
----
- 1
–
 
 
=

depending on the approximations used.
For each length l of the rod the measured resistance value R determines the apparent resistivity value ρ which when
plotted against l provides a visual aid for determining earth resistivity variation with depth. For more clarity, suppose
that the field tests gave the curve shown in Fig 4. By inspection of the curve it can be concluded that soil structure is
at least three distinct layers. For small values of l (2 to 5 m) soil has a resistivity value of 210 Ω.m. The middle layer
resistivity is about 2 to 2.5 times that of the top layer. The thickness of this middle layer is not easy to determine by
visual inspection of the curve. The third layer is very conductive. Its resistivity value is certainly less than 100 Ω.m.
However, the exact value cannot be obtained through visual inspection. Two solutions are then possible:
1) Continue measurements with rods driven deeper into the soil
2) Use analytical techniques to compute, from the measured data, an equivalent earth structure
Figure 4—Variation of Depth Results
Additional measurements will certainly help in obtaining the third-layer resistivity. However the thicknesses of the two
first layers are still not easy to determine. Moreover, driving rods to great depth may be difficult and expensive. Other
alternatives consist of assuming earth as uniform, two-layer structured (or more), and being composed of a material
whose resistivity varies with depth according to a simple mathematical law (linear, exponential...).
The resistance of a rod in such earth. models is known or can be easily calculated (see Appendix B). Using a simple
computer program or simply by a cut-and-try method, the best fit to the experimental results can be obtained (see
Appendix B).
As already mentioned, the variation of depth method fails to predict earth resistivity at large distances from the area
where the test rod is embedded (distances larger than 5' to 10 times the driven rod length).
Since this method is suited only for determining the resistivity of small volumes of soil, it is not recommended that
extrapolation of the results be attempted.
7.3.4 Four-Point Method
The interpretation of the four-point method is similar to that of the method described in 7.3.2. For example, in the case
of the Wenner arrangement, the measured apparent resistivity is plotted against the electrode spacing a. The resulting

curve then indicates the soil structure. Again the depths of various layers are not easy to determine by visual inspection
of the curve. Many authors [B21], [B39] give quick empirical rules to help in establishing the layer thickness. For
example:
1) The Gish and Rooney method [B21]; from the resistivity curve, a change in formation, for example, another
layer is reached at a depth equal to any electrode separation at which a break or change in curvature occurs.
2) The Lancaster-Jones method [B28]; the depth to the lower layer is taken as 2/3 the electrode separation at
which the point of inflexion occurs.
However, a better solution assumes an earth model such as:
a) Uniform resistivity
b) Horizontal layers of uniform resistivities (see Appendix A)
c) Exponential variation of the resistivity (see Appendix A)
For each model the mathematical relation between the apparent resistivity and the various earth parameters must, of
course, be known or be easy to calculate. Some analytical methods frequently used are described in Appendix C.
The solutions are given for an exponential and two layer-soil model. Using an adequate analytical method, the best fit
to the experimental data gives the required earth parameters (Fig 5 shows the results obtained using models 2 and 3).
The best model to use depends on the purpose of the measurements. Often a two-layer earth model gives excellent
results [B39].
Figure 5—Example of an Earth Resistivity Interpretation

7.4 Instrumentation
Shepard-soil resistivity meter or similar (see 7.2 for complete description).
7.4.2 Four-Point or Variation-of-Depth Methods
One of the following instruments can be used (see Section 12).
1) Power supply with ammeter and high impedance voltmeter
2) Ratio ohmmeter
3) Double-balance bridge
4) Single-balance transformer
5) Induced-polarization receiver and transmitter.
Dependent on the mode of connection and terminals used these instruments can either measure ground resistance or
earth resistivity.
In inductive coordination work, spacings up to 1000 m often have been used. For these long spacings, the resistance is
of the order of a few hundredths of an ohm, and a sensitive direct-current potentiometer with a battery supply as high
as 180 V may be required. For the shorter spacings, the four-terminal instruments shown in Figs 14, 15, and 16 are
convenient and adequate. For some instruments correction may be required for the potential probe resistances; in such
cases correction factors can usually be obtained from the supplier of the instrument.
The induced polarization transmitter is normally rated at a few hundred watts. However, for great spacings or
extremely high top-soil resistivities, units rated at more than 1000 W may be necessary
8. Ground Impedance
8.1 General
Connections to earth in general are complex impedances, having resistive, capacitive, and inductive components, all of
which affect their current-carrying capabilities. The resistance of the connection is of particular interest to those
concerned with power frequencies because it is affected by the resistivity of the earth in the area of the connection. The
capacitance and inductance values are of interest to those concerned with higher frequencies, such as are associated
with radio communications and lightning.
Ground-impedance measurements are made:
1) To determine the actual impedance of the ground connections
2) As a check on calculations
3) (3) To determine (a) the rise in ground potential and its variation throughout an area, that results from ground
fault current in a power system, (b) the suitability of a grounding connection for lightning protection, and the
suitability of a grounding connection for radio-frequency transmission at a transmitter
4) To obtain data necessary for the design of protection for buildings, the equipment therein, and any personnel
that may be involved
Ground connections of all power and communication systems should be studied to determine the variation in ground
potential that can be encountered during ground-fault conditions so as to ensure personnel safety, adequacy of
insulation, and continuity of service.

8.1.1 Characteristics
The characteristics of a grounding connection vary with the composition and physical state of the soil as well as with
the extent and configuration of the buried electrode. Earth in any given locality is composed of various combinations
of dry earth, swampy ground, gravel, slate, sandstone, or other natural materials of widely varying resistivity. It may
be relatively homogeneous over a large area, or it may be effectively saucered in granite, sand, or other matter having
a high resistivity and thus be practically insulated from the surrounding area. Consequently, the characteristics of a
grounding connection (ohmic resistance) vary with the seasons, which affect temperature, moisture content, and
compactness of the soil.
Calculations and experience show that, in a given soil, the effectiveness of a ground grid is dependent largely upon the
overall size of the ground grid. The addition of buried conductors and driven rods within an enclosure also aid
somewhat in reducing the ground impedance. This reduction diminishes with the addition of each successive
conductor or rod. A good method for reducing the ground resistance of a transmission-line tower or mast is to install
radial counterpoises.
After the installation of a substation or other grounded structure, the settling of the earth with annual cyclical weather
changes tends to reduce the ground impedance substantially during the first year or two.
The impedance of a grounding electrode is usually measured in terms of resistance because the reactance is generally
negligible with respect to the resistive component. (This is not applicable for large grounding structures with
impedance values below 0.5 Ω, and for grounds subject to surge or impulse currents.) This resistance will not usually
vary greatly from year to year after the first year or two following the burial of the ground grid. Although the ground
grid may be buried only half a meter below the surface, the variation of the resistance for larger stations seems to-bear
little relationship to the variation of the resistivity at the burial level. This is especially true for grids equipped with
long driven rods in contact with the deep soil which normally is not influenced by weather conditions (temperature and
moisture changes which result in top layer resistivity variations). However, this will not be true for grids buried over a
high resistivity stratum, or simply for small electrodes (having an area of less than 50 m2
).
Although the above statements appear to be contradictory they are, nevertheless, true. Records which have been kept
of large area ground grids over a period of eighteen years show little variation in the measured value of resistance,
whereas, resistivity measurements in the same area show wide variations (as much as 17 to 1 at shallow depths). It
should be recognized that the resistance of a grounding connection with a small number of driven rods may vary more
closely with that indicated by resistivity measurements. This indicates that the resistance of large area ground grids is
proportional to resistivity measurements made for greater depths where less variation is encountered.
Some of the ground-fault current from a transmission line fault to a substation ground grid tends to follow the
transmission line. Depth of mean current path is directly proportional to the square root of the earth resistivity and
inversely proportional to the square root of the frequency. Thus resistance tends to increase the cross-sectional area of
the current path, whereas inductance tends to decrease it and to tie more closely to the transmission line. This tendency
will also affect the pattern of the current path away from the electrode.
8.1.2 Theoretical Value of Ground Resistance
Calculated or theoretical values of the resistance of an electrode to remote earth can vary considerably from the
measured value because of the following factors:
1) Adequacy of the analytical equations used in the resistance calculations.
2) Conditions of the soil at the time the measurement is made. Earth resistivities being different from those
assumed in the calculations.
3) Inaccurate or insufficient extent of the resistivity survey; for example, number and dispersal of tests, probe
spacings, and inadequacy of the instrumentation used.
4) Presence in the soil of adjacent metallic buried structures and ground wires which may divert a substantial
amount of the test current.

In order to decrease the sources of error in establishing the relationship between earth resistivity and ground resistance
it is advisable to take resistivity and resistance measurements under similar weather and moisture conditions.
If the measured values are used as data for the design of a grounding electrode, it is recommended that the
measurements be carried out under various weather conditions. This will help the designer in establishing the most
restrictive or limiting case, especially for small grounds which are influenced by seasonal changes in weather.
8.2 Methods of Measuring Ground Impedance
8.2.1 General
In this section only general methods are covered [B6], [B8], [B12], [B31], [B30]. For the instrumentation available
refer to Section 12. While in this section the ohmic value is called resistance, it should be remembered that there is a
reactive component that should be taken into account when the ohmic value of the ground under test is less than 0.5 Ω,
and the ground is of a relatively large extent. This reactive component has little effect in grounds with an impedance
higher than 1 Ω. The resistance of a ground electrode usually is determined with alternating or periodically reversed
current to avoid possible polarization effects when using direct current. The frequency of this alternating current
should be near the power frequency.
8.2.1.1 Two-Point Method (Ammeter-Volt-meter Method)
In this method the total resistance of the unknown and an auxiliary ground is measured. The resistance of the auxiliary
ground is presumed to be negligible in comparison with the resistance of the unknown ground, and the measured value
in ohms is called the resistance of the unknown ground.
The usual application of this method is to determine the resistance of a single rod-driven ground near a residence that
also has a common municipal water supply system that uses metal pipe without insulating joints. The water pipe is the
auxiliary ground and its ground resistance is assumed to be in the order of 1 Ω and must be low in relation to the
permissible driven ground maximum resistance which is usually in the order of 25 Ω.
Obviously, this method is subject to large errors for low-valued driven grounds but is very useful and adequate where
a go, no-go, type of test is all that is required.
8.2.1.2 Three-Point Method
This method involves the use of two test electrodes with the resistances of the test electrodes designated r2 and r3 and
with the electrode to be measured designated r1. The resistance between each pair of electrodes is measured and
designated r12, r13, and r23,
where
r12 = r1 + r2 etc. Solving the simultaneous equations, it follows that:
(7)
Therefore, by measuring the series resistance of each pair of ground electrodes and substituting the resistance values
in the equation, the value of r1 may be established. If the two test electrodes are of materially higher resistance than the
electrode under test, the errors in the individual measurements will be greatly magnified in the final result. For the
measurement, the electrodes must be at some distance from each other; otherwise absurdities may arise in the
calculations, such as zero or even negative resistance. In measuring the resistance of a single-driven electrode the
distance between the three separate ground electrodes should be at least 5 m with a preferable spacing of 10 m or more.
For larger area grounding systems, which are presumably of lower resistances, spacings in the order of the dimensions
r1
r12
( ) r23
( ) r13
( )
+
–
2
------------------------------------------------
-
=

of the grounding systems are required as a minimum. This method becomes awkward for large substations, and some
form of the fall-of-potential method is preferred, if high accuracy is required.
8.2.1.3 Ratio Method
In this method the resistance of the electrode under test is compared with a known resistance, usually by using the
same electrode configuration, as in the fall-of-potential method. Since this is a comparison method the ohm readings
are independent of the test current magnitude if the test current is high enough to give adequate sensitivity.
8.2.1.4 Staged Fault Tests
Staged high-current tests may be required for those cases where specific information is desired on a particular
grounding installation. Also, a ground impedance determination can be obtained as auxiliary information at the time of
actual ground faults by utilizing an oscillograph or one element of the automatic station oscillograph.
In either case the instrumentation is the same. The object is to record the voltage between selected points on one or
more oscillograph elements. The voltages to be recorded will probably be of such great magnitude that potential step-
down transformers will be required. The maximum voltages that can be expected and thus the ratios of the potential
transformers required may be determined in advance of the staged tests by using the fall-of-potential method at
practical values of test current.
Another important consideration is the calibration of the oscillograph circuit, which is composed of a potential
transformer with a possible high resistance in the primary. This resistance is composed of the remote potential ground
in series with a long lead. A satisfactory calibration of the deflection of the oscillograph element may be made by
inserting a measured voltage in the primary circuit in series with the lead and the remote potential ground as used
during the test.
The location of the acutal points to be measured is dependent on the information desired; but in all cases due allowance
must be made for coupling between test circuits, as given in 6.5.
8.2.1.5 Fall-of-Potential Method
This method has several variations and is applicable to all types of ground impedance measurements. As mentioned in
6.5, the impedance of a large grounding system may have an appreciable reactive component when the impedance is
less than 0.5 Ω, therefore, the measured value is an impedance and should be so considered although the terminology
often used is resistance.
The method involves passing a current into the electrode to be measured and noting the influence of this current in
terms of voltage between the ground under test and a test potential electrode.
A test current electrode is used to permit passing a current into the electrode to be tested (see Fig 6).
The current I through the tested electrode E and the current electrode C, results in earth surface potential variations.
The potential profile along the C, P, E, direction will look as in Fig 7. Potentials are measured with respect to the
ground under test, E, which is assumed for convenience at zero potential.
The fall-of-potential method consists of plotting the ratio of V/I = R as a function of probe spacing x. The potential
electrode is moved away from the ground under test in steps. A value of impedance is obtained at each step. This
impedance is plotted as a function of distance, and the value in ohms at which this plotted curve appears to level out
is taken as the impedance value of the ground under test (see Fig 8).

Figure 6—Fall-of-Potential Method
Figure 7—Apparent Resistance for Various Spacings X

Figure 8—Case of a High-Impedance Ground System
This rule of thumb must be applied carefully since it gives satisfactory results only if a flat portion has been established
very clearly. The theory of the fall of potential method is explained in Appendix C.
In order to obtain a flat portion of the curve it is necessary that the current electrode be effectively outside the influence
of the ground to be tested. This influence is sometimes called extent of station ground and may be considered as the
distance beyond which there is a negligible effect on the measured rise of ground voltage caused by ground current.
Theoretically the influence extends to infinity; but practically there is a limit, because the influence varies inversely as
some power of the distance from the ground to be tested. This influence is determined and allowed for during the test
on ground grids or deep-driven ground rods of 1 Ω or less. In the case of small-area, such as single rod driven
grounds, tower footings (not connected to overhead wires or counterpoises) the influence can be rendered negligible
by keeping spacings in the order of 50 m which is practical and easy to achieve on site.
For large grounds the spacings required may not be practical or even possible. Consequently the flat portion of the
curve will not be obtained and other methods of interpretation must be used.
It is important to note at this stage that theoretical analysis of the fall of potential problem [B14], [B19], [B40], [B41],
shows that placement of the potential probe P at the opposite side with respect to electrode C (P2) will result always in
a measured apparent resistance smaller than the true resistance.
Moreover, when P is located on the same side as electrode C but away from it (P1), there is a particular location which
gives the true resistance.
It should be emphasized, however, that the P2 arrangement presents the advantage of minimizing the coupling problem
between test leads. If reasonably large distances between P2 and C are achieved (with respect to the electrode E under
tests), then it is possible to use this method to obtain a lower limit for the true resistance of electrode E.
A representative curve for a large grid ground is shown in Fig 9. The data for this figure were taken from a test made
on a station that had a ground grid approximately 125 m by 150 m. Distances were measured from the station fence;
hence the impedance is not zero at zero distance on the curve. Curve B is obtained with the potential probe located
between E and C. Curve A is obtained with the potential probe located at the opposite side with respect to the current
electrode C.

The test shows the existence of a mutual resistance between the current electrode and the station ground and that is
why curve B does not level out. Curve A does seem to level out and can be used to obtain a lower limit for the
impedance value of the electrode under test.
Figure 9—Case of a Low-Impedance Ground System
8.2.1.6 Interpretation of the Results
Appendix C shows that there is one potential probe spacing which gives the true ground impedance of the ground
being tested.
The correct spacing may be very difficult, however, to determine especially if the ground grid has a complex shape (see
[B8], [B12] and [B14] for additional information). The correct spacing is also a function of the soil configuration as
demonstrated in [B12] and illustrated by Fig 10, which is applicable to small ground systems. As indicated in this
figure the required potential probe spacing x (when the probe is between E and C and when the soil is uniform) is such
that the ratio x/d = 0.618. This was first proved by E.B. Curdts [B8] for small hemispherical electrodes.
The above statements show that in order to apply the 61.8% rule the following conditions should exist:
1) A fairly uniform soil
2) Large spacings so that the electrodes may be assumed hemispherical.
Also the reference origin for the measurement of spacing must be determined. For hemispherical grounds, the origin
is the center of the ground. For large ground systems some authors introduce the concept of electrical center and a
method of determining the impedance of extensive ground systems imbedded in a uniform soil (based on the concept
of electrical center) is described in a paper by Thug [B40]. It should be noted, however, that there is no proof that the
electrical center is a physical constant (such as gravity center) which is not influenced by the current electrode location
and characteristics.
As a general conclusion, the best guarantee of a satisfactory measurement is to achieve a spacing such that all mutual
resistances are sufficiently small and the fall-of-potential curve levels out. The main advantage of the fall of potential

method is that the potential and current electrodes may have a substantially higher resistance than the ground being
tested without significantly affecting the accuracy of the measurement.
Figure 10—Required Potential Electrode Position in a Two Layer Earth
8.3 Testing the Integrity of the Ground Grid
In this test the object is to determine whether the various parts of the ground grid are interconnected with low-
resistance copper. This copper is shunted by the surrounding earth, which usually has a very low impedance.
The best method for making integrity-of-ground-grid tests is to use a large but practical direct current and some means
of detecting the voltage drop caused by this current. Direct reading ohmmeters can be used if the sensitivity is
adequate.
The ammeter-voltmeter method, using alternating current, cannot be used satisfactorily for this test. The reactance of
a large copper wire in this case is shunted by the surrounding earth, a path which may have slightly less reactance than
the wire. Therefore, a continuity test for buried wire would give indeterminate results if alternating current were used.

By extension of this reasoning, one concludes that it is practically impossible to sensibly lower the impedance between
two ground grids which are any distance apart, each of which has an impedance in the order of 0.1 Ω at 60 Hz. The
addition of copper connectors, however large, will not lower the reactance between the two ground grids. The resistive
component can be lowered by additional connectors, and this component is used to determine the integrity of the
ground grid.
One practical integrity test consists of passing about five amperes into the ground grid between two points to be
checked. The voltage drop across these points is measured with a millivoltmeter or portable potentiometer and the
effective resistance is calculated from the current and voltage readings. From these readings and the calculated
resistance of copper it can be determined whether there is an adequate connection. For those ground systems that have
a direct voltage between points, the change of voltage caused by the test current is used to calculate the resistance.
For the majority of large ground systems in service there will be a realtively large alternating voltage between the
points to be measured compared with the direct millivolts to be detected. The effects of the alternating component on
the detector can be mitigated by shunting the moving coil in the millivoltmeter, or the galvanometer in the
potentiometer, with a capacitor of 20 µF or more. This capacitor should preferably have a liquid impregnated paper
dielectric, but some modern electrolytic condensers have so little leakage that they can be used in this application.
8.4 Instrumentation
The instruments used for ground resistance measurements are identical to those used for resistivity measurements.
These instruments are described in Section 12.
9. Earth Potential
9.1 Equipotential Lines
As a result of current from an electrode to earth and through its earth path, equipotential surfaces plotted at right angles
to these current lines will assume a shape controlled by the path of the current. The density of equipotential surfaces,
having equal voltage differences between them, across a path in a given direction determines the step voltage which
may be encountered. This gradient will be highest near the grounding electrode.
The distance between equipotential surfaces, measured along the surface of the earth radially from the grounding
connection, will vary with a number of factors. These include variations in resistivity of the earth, the presence of
buried pipes, conduit, railroad rails, steel fences, metallic cable sheaths, and the presence of overhead lines carrying
ground current.
As indicated in 8.1, some of the ground-fault current tends to return to the source under the transmission line which
carries the current. Consequently it will be found that the ground potential under the transmission line carrying fault
current will have a steeper gradient than in the adjoining earth. This results in changing the pattern of the equipotential
lines whenever a different transmission line terminating at the station is faulted. Therefore, equipotential lines cannot
be established simply by measuring resistance from the grounding connection to various points around it.
When once established, the voltage between the equipotential lines for a given fault condition can be expected to vary
directly with ground-fault current magnitude. This assumes no change in the resistivity of the earth around the
grounding system during the flow of fault current.
9.2 Potential Contour Surveys
A potential contour survey is made to locate possible hazardous potential gradients in the vicinity of grounded
electrical structures during fault conditions [B7], [B29]. The voltage drop to points surrounding the structure is

measured from a known reference point and plotted on a map of the location. A potential contour map may then be
drawn by connecting points of equal potential with continuous lines. If the contour lines have equal voltage differences
between them, the closer the lines, the greater the hazard. Actual gradients due to ground-fault current are obtained by
multiplying test current gradients by the ratio of the fault current to test current.
The most accurate measurements of potential gradients are made with the voltmeter-ammeter method. A known
current, between 50 A and 100 A, held constant during test, is passed through the ground grid to a remote ground test
electrode and returned through an insulated conductor.A remotely located ground test electrode is necessary to prevent
gradient distortion, caused by the mutual impedance of inadequately spaced ground electrodes. This distance may vary
from 300 m, for a small ground grid to a mile or more for larger installations. Measurements should be made with a
very-high-impedance voltmeter on the surface of the earth along profile lines radial to the point of connection to the
ground grid. Unless suitable means are employed to mask out residual ground current, the test current must be of
sufficient magnitude to do so. At the same time care must be taken to prevent heating and drying of the soil in contact
with the ground grid or test electrode to avoid variations in voltage gradients in a series of measurements. Economics
and the necessary detail required will determine the number of measurements to be made.
When more than one overhead line or underground cable are connected to a substation, potential gradients in and
around the substation may be quite different for faults on different lines or cables. Likewise, faults at different
locations in large substations may result in differences in potential gradients in and around the substation. It may,
therefore, be advantageous to determine potential gradients in and around a large substation for two or more fault
conditions.
Underground metallic structures, for example, neutral conductors, metallic cable sheaths, metallic water and gas lines,
etc, metallic structures on the surface of the ground such as railroad rails and fences, and overhead ground wires in the
vicinity of a substation, whether connected to the ground grid or not, will usually have a significant effect on potential
gradients and should be considered when making potential gradient measurements.
When a potential gradient survey cannot be justified economically, potential gradients may be calculated from ground
resistance or soil resistivity measurements. The accuracy of such calculations will be dependent upon the accuracy of
the measurements, and the unknown abnormalities of the earth around and below the ground grid.
The adequacy of such calculations may be verified with relatively few potential gradient measurements.
9.3 Step and Touch Voltages
The magnitude of step and touch voltage (see Fig 11) may be scaled off of a potential contour map of the site or
actually measured by the voltmeter-ammeter method. These values are proportional to the earth current and (provided
that the deep soil resistivity is constant) to the top soil resistivity.
NOTE — A variation of resistivity of the top soil in some cases increases the ground resistance. This in turn may cause a variation
in the earth current. The changes in step and touch voltages should therefore be determined by taking into account
simultaneously, top-soil resistivity and earth current variations.

Figure 11—Step and Touch Voltages

10. Transient Impedance
10.1 Transient Impedance of Ground Systems
10.1.1 General
Many grounding systems are designed for operation under transient conditions, most commonly for carrying impulse
current due to a lightning stroke. It has been shown [B4], [B15] that the impedance of a simple grounding electrode
depends on the amplitude of the impulse current and also varies with time, depending on the impulse form.
The nonlinearity of the grounding impedance is caused by local discharges in soil in the area where the electric field
gradient exceeds 2.5 k–3 kV/cm. Since the field gradient attains the highest value at the ground electrode the
discharges partly short circuit the layer of soil adjacent to the electrode. Consequently the transient impedance of the
grounding system for high-current impulses is lower than the value measured with the conventional steady-state
methods, or with an impulse of lower amplitude which does not produce the discharges in soil.
An opposite effect has been observed in the case of extended ground electrodes, wires or strips more than 300 m (1000
ft) long, when tested with steep front impulses. The voltage drop across the grounding impedance shows then a large
inductive component. The instantaneous impedance is normally determined as a quotient of the applied transient
voltage and current recorded at the same instant. The additional voltage component which appears across the
grounding inductance at the steep impulse front (or at an abrupt collapse of the impulse current) is then interpreted as
an increase of the grounding impedance.
10.1.2 Measurements of the Transient Impedance of Ground Systems
The grounding impedance measurements have to be performed using the real amplitude voltage and current impulses,
because the nonlinear characteristics of this impedance exclude modeling techniques or reduced scale experiments. To
perform such measurements a testing circuit is required which contains a high-voltage impulse current generator of
adequate energy, as well as a precise voltage divider, current measuring shunt, and double beam impulse oscillograph.
The lightning current ranges between 1 kA and 100 kA and a typical grounding impedance is of the order of 10 Ω.
Considering these typical requirements a mobile impulse generator which is normally used by power utilities for
testing of insulation coordination in high-voltage substations can be suitable for measurements of the transient
grounding impedance. Another possible solution consists of installing a prototype ground system in the soil near a
high-voltage laboratory and connecting the laboratory generator, as well as the measuring apparatus, to the ground
system under test.
The simultaneous oscilloscope recording of the voltage drop across the grounding impedance, and of the applied
impulse current, requires a reference grounding point. The reference ground can be conveniently located at the impulse
generator base, provided that there is sufficient distance to the examined ground. The transient impedance of ground
is derived from the voltage and current oscillograms as a quotient of these two transients, calculated point by point for
consecutive time intervals.
Since the variation of the grounding impedance depends on the impulse current amplitude and form, as well as on the
electrode geometry and the type of soil, several measurements have to be taken to permit a more general interpretation
of results and for a definite conclusion.
Attention should also be drawn to possible common mode interference which may appear in the measuring circuit if
the grounding points of the voltage divider and shunt are shifted from the reference ground potential.
10.1.3 Instrumentation
The schematic diagram of the apparatus used is given in Fig 12.

Measurement of transient impedance of a driven grounding rod or of a distributed ground system requires specialized
equipment, which is normally used in high-voltage laboratories. The high-voltage and high-current impulse is
generated by discharge of a large capacitor into an impulse forming network. Although such a circuit can be
improvized on the test site, in most practical cases a mobile impulse generator is used. There are no generally accepted
standards for the current impulse form but the 8/20 µs or 4/10 µs impulse is frequently applied for measurements of the
transient grounding impedance.
Apart from the ground to be measured the test circuit has to have another auxiliary ground which carries the return
current from the impulse generator. This ground is preferably of the distributed type, such as a substation or a
laboratory grounding mesh, and its impedance must be significantly lower than that of the measured ground.
The impulse generator is connected to this ground through a high-current shunt. The unit response of the shunt has to
comply to the requirements of ANSI/IEEE Std 4-1978, IEEE Standard Techniques for High-Voltage Testing. Voltage
drop across the resistance of the measured ground is measured by a voltage divider preferably of the resistive type and
designed for the expected voltage range. It is essential to keep the shunt and the divider grounding points directly
connected to the auxiliary ground by short, low-inductance leads.
Figure 12—Measuring Circuit for Recording the Transient Impedance of Driven Grounds
The divider measuring properties should comply with the requirements of ANSI/IEEE Std 4-1978 and the conductor
running from the divider to the ground being measured should be kept as short as possible.
The simultaneous recording of the voltage and current impulses is normally performed with a double beam
oscilloscope. The two coaxial cables connecting the divider and the shunt to the oscilloscope have to be of the same
length to avoid time lags between the recorded transients. This is a particularly important requirement since the

grounding impedance curve is plotted as a quotient of instantaneous values of the recorded voltage and current and
even a small shift of their respective time scales may result in a considerable error.
Taking into account the nonlinear character of the transient grounding impedance, the measurements should be
performed at different impulse current shapes and amplitudes. Each set of recorder oscillograms permits plotting a
family of the grounding impedance curves, which will characterize the performance of the grounding at the high- and
low-impulse currents.
11. Model Tests
11.1 Purpose
The main purpose of a model test is to help predict the probable resistance to true earth of a complex ground electrode
or to predict the probable voltage gradient of a complex ground system [B1], [B11], [B13], [B25], which otherwise
cannot be calculated accurately.
11.2 Similarity Criteria and Limitations
The work starts by establishing the earth structure to be modeled; the reduced model will then have to obey certain
laws [B11]:
1) All the geometrical dimensions of the earth model and of the test electrode should be scaled according to one
unique factor µL.
2) When the model consists of several layers of soil, the ratio of each layer resistivity to a reference layer should
be equal to the ratio of their respective real life counterparts. The ratio of the real case to the model reference
layer determines the resistivity scale factor µρ
When the above is completed the following precautions should be observed so as to minimize the errors caused by the
finite size and limitations of the electrolytic tank.
a) Alternating current should be used to prevent polarization of electrodes which would cause errors at low
currents.
b) Current densities should be kept less than 0.1 A/cm2
of electrode.
c) The probe should be about 3 mm diameter round rod cut off square and should not be immersed more than
3 mm.
d) The model should be to scale and large enough to simplify its manufacture and assure a reasonable accuracy,
but should be small enough to be convenient. A 20 to I scale is often satisfactory.
e) The tank dimension should not be smaller than five times the model's maximum dimensions. This will give
error of less than 10% of results obtained from an infinite tank.
11.3 Instrumentation
The materials required for model test are (see Fig 13):
1) A tank of nonconducting material
2) Various materials arranged adequately in the tank to constitute the layers of the earth to be modelled. The top
layer should preferably be water with some quantity of common salt or copper sulfate to achieve the desired
resistivity. The second layer could be simulated by a concrete block of appropriate dimensions.
3) A scale model of the ground to be tested.
4) An alternating current source of power with some means of varying the voltage. Use of a frequency in the
range of 500 Hz to 1000 Hz aids in eliminating electrolytic polarization which causes potential distortions.

5) A voltmeter with a minimum input impedance of 5Ω/V, or better, a potentiometer with an oscilloscope null
detector.
6) A return path plate and a small wire probe.
Figure 13—Electrolytic Tank
11.4 Resistance Measurements
1) Suspend the scale ground model and the plate at A and B (AB should be at least 3 to 4 times the model ground
dimension).
2) Inject a small current I between A and B (0.1 to 0.5 A).
3) Locate the probe P between A and B so that AP = 0.618 AB. Measure the voltage V between P and A.
4) The scale model ground resistance is (see Appendix C):
(8)
11.5 Potential Measurements
Using the model ground as the reference potential (zero potential), the electrolyte surface potential at any location can
be measured simply by moving the probe P on the surface of the electrolyte. When a null detector and potentiometer
are used, R1(R1+R2 = R = constant) is adjusted so that the current through the null detector is minimum. The measured
potential VS is then in %: R1/R, and in volts: RlVp/R .
11.6 Interpretation of Measurements
The model results must be transformed to the real life case [B11]:
Let:
µL =Lreal/Lmodel (length)
µρ =ρreal/ρmodel ( reference resistivity)
µI =Ireal/I model (current)
RA V I
⁄
=

be the modelling scale factors, then the real life resistance is:
(9)
and the real life potential is:
(10)
12. Instrumentation
12.1 Ratio Ohmmeter
A commonly used instrument for measuring ground resistance is shown in Fig 14.
Current from the hand-cranked direct-current generator is reversed periodically by the current reverser and exists in the
earth between ground X under test and current electrode C. The fall-of-potential between X and the potential electrode
P is rectified by the potential reverser, which is on the same shaft, and therefore, operates in synchronism with the
current reverser. The coils operate in a field provided by a permanent magnet. The Current coil tends to turn the pointer
toward zero, while the potential coil tends to turn the pointer toward a higher ohm reading. The operating current
through these coils is furnished respectively by the current through and the voltage drop across the ground under test,
therefore, the scale of the instrument can be calibrated in ohms. A suitable range switch provides a divider to the scale
values.
Figure 14—Ratio Ohmmeter
Rreal Rmodelµρ µL
⁄
=
Vreal VmodelµIµρ
µL
⁄
=

Ieee81 1983

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